Desktop Environments

A desktop environment is a complete suite of software designed to maintain a certain experience in a Linux environment. It will contain a display manager, window manager, session manager, file manager, and various other default applications that a user may find useful (web browser, audio player, etc). A desktop environment is not a required part of a Linux experience, although most Linux distributions will include one by default. It is entirely possible to have a working graphical environment without installing a desktop environment, instead opting to only use a window manager and utilities that you require, and many users choose to do this.

LXDE is the most minimal DE around. If you are running on a toaster supercluster or just need the most battery life out of your freedom device, and are too lazy/dumb to setup a WM, LXDE is the only correct choice.

Display Managers

A display manager is what might typically be thought of as a "login screen". It will prompt you to choose a user to log in as, as well as specify a session to be used, which allows you to switch between desktop environments easily.

LightDM

SLiM

KDM - Display manager used in KDE.

GDM - Display manager used in GNOME.

Window Managers

Currently most GNU/Linux distributions use the X Window System for drawing the desktop (with Wayland being planned to replace it later). The X.org Server is the most common implementation of the X Window System. It is designed to be modular and highly customizable. One of the results of this design is that X.org doesn't manage windows. Instead it depends on a special client application called a window manager. The window manager (WM in short) moves and resizes windows, among other things, often in response to user input. Window managers also do much more, like automatic window layout, compositing, drawing decorations, drawing panels, providing multiple workspaces, and so on.

Window managers can be divided into these three categories:

Stacking - They allow windows to draw their contents one on top of another on the desktop, starting with the one on the bottom and going up in the "Z order".

Compositing - Provide a buffer for each window to draw on and then compose those buffers together creating the desktop image. This type of window manager allows use of semitransparent windows.

Tiling - The windows do not overlap.

Compiz's expo plugin. As most window managers, it allows for multiple workspaces, as seen here.

Static tiling WMs such as ratpoison always use a set number of equal size tiles, and the tiles do not move

Dynamic tiling WMs such as awesome allow you to change the layout of the tiles, the number of tiles onscreen, and other things. it should be noted that awesome also has a stacking mode in addition to many tiling configurations.

Many WMs contain both stacking and tiling modes, and the behavior can be switched by the user.

It's also possible for WMs that don't tile windows to use a separate application that works together with the main window manager to automatically tiles windows (for example: pytyle).

Finally, there are also composite managers such as xcompmgr that work together with a non-compositing WM making it compose windows, allowing for effects such as transparency and drop shadows.

Compiz - A compositing WM being developed since 2006. It uses OpenGL (AIGLX). It is know for having a lot functionality and providing many interesting effects. However, it can cause problems if the graphics are faulty.

KWin - A compositing WM used in KDE. It's comparable in feature set to compiz.

Themes

There are two main toolkits you need to concern yourself with styling: GTK and Qt. Luckily, there are themes for both that will adapt to the other. So find a theme for whichever toolkit your distro uses prominently. For KDE based distros, that's Qt. For everything else, that's GTK.

GTK Themes

There are a number of great themes. All of these are GTK3 compatible. To apply them, see GTK Theming.